rotating a tensor where the tensor elements are functions of a third index (conceptually)

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Lloyd Bumm
Lloyd Bumm 2019-11-20
I have a 3x3 tensor "A" where the elements are a functions of wavelength (e.g. 1000 deep). I need to rotate the tensor, R*A*R', then do other operations. Here R is the usual 3x3 rotation matrix. It would be most convenient to have the tensor look like:
A = [ axx(k), 0(k), 0(k);
0(k), ayy(k), 0(k);
0(k), 0(k), azz(k) ];
I can do all this my looping over k and treating each k-layer as a 3x3, but is there a better way?
There are really 2 questions.
1) Is there a more efficient way to load the 3x3xk array from 1D vectors of axx(k), ayy(k), and azz(k), compared to constructing each k-layer one at a time in a for loop?
2) Is there a way to do the rotation of A (the 3x3xk matrix) without doing the rotation one 3x3 layer at a time in a for loop?

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